Hybrid FVM-LBM schemes are developed in the past few years to use capabilities of both Navier-Stokes based finite volume method (FVM) and lattice Boltzmann method (LBM) to solve macro-meso multiscale problems. In this scheme, the major task is to develop some lifting relations that reconstruct distribution functions in LBM sub-domain from macroscopic variables and their derivatives. The macroscopic variables are computed using Navier-Stokes based FVM in macroscale sub-domain, while distribution functions are computed using LBM in mesoscale sub-domain. The pioneer works in this area used the single relaxation time (SRT) version of LBM. However, it is known that the numerical stability and accuracy of the multiple relaxation time (MRT) version of LBM is superior to the SRT one. Based on this fact, a new hybrid FVM-LBM scheme based on the MRT version of LBM for fluid flow simulation is proposed in our previous work. But, our previous hybrid scheme is limited to fluid flow problems. In the present research, some additional lifting relations are developed to extend the working area of our previous hybrid FVM-LBM (MRT) scheme to heat and mass transfer problems. The computational efficiency of the resulting hybrid method is proved by comparing its CPU time with those of LBM and Navier-Stokes based FVM for a sample meso-macro scale problem. Afterward, the new hybrid scheme is validated in two and three dimensions by solving three benchmark heat transfer problems. Additionally, to indicate the applicability of the present hybrid scheme in a meso-macro scale problem, three-dimensional heat transfer from a porous heat sink is simulated in pore scale. The fluid-solid conjugate heat transfer inside porous media is simulated using LBM, while the surrounding free fluid region is simulated using Navier-Stokes based FVM. The results indicate the superiority of the proposed new hybrid scheme over the previous ones. (C) 2019 Published by Elsevier Ltd.